 Decoherence-free subspace

A subspace on which every operator in a specified noise model acts as a common scalar, so the encoded density operator is preserved without syndrome-dependent recovery. For collective $z$ rotations, the span of $|01⟩$ and $|10⟩$ has zero total $Z$ eigenvalue and is invariant. Protection depends on the collective-noise assumption; independent local rotations do not generally preserve its logical phase.